Abstract: In this paper the optimal control strategies of an SIR (susceptible-infected-recovered) epidemic model with time delay are introduced. In order to do this, we consider an optimally controlled SIR epidemic model with time delay where a control means treatment for infectious hosts. We use optimal control approach to minimize the probability that the infected individuals spread and to maximize the total number of susceptible and recovered individuals. We first derive the basic reproduction number and investigate the dynamical behavior of the controlled SIR epidemic model. We also show the existence of an optimal control for the control system and present numerical simulations on real data regarding the course of Ebola virus in Congo. Our results indicate that a small contact rate(probability of infection) is suitable for eradication of the disease (Ebola virus) and this is one way of optimal treatment strategies for infectious hosts.

Abstract: Constraint-based approaches recently brought new insight into our understanding of metabolism. By making very simple assumptions such as that the system is at steady-state and some reactions are irreversible, and without requiring kinetic parameters, general properties of the system can be derived. A central concept in this methodology is the notion of an elementary mode (EM for short) which represents a minimal functional subsystem. The computation of EMs still forms a limiting step in metabolic studies and several algorithms have been proposed to address this problem leading to increasingly faster methods. However, although a theoretical upper bound on the number of elementary modes that a network may possess has been established, surprisingly, the complexity of this problem has never been systematically studied. In this paper, we give a systematic overview of the complexity of optimisation problems related to modes. We first establish results regarding network consistency. Most consistency problems are easy, i.e., they can be solved in polynomial time. We then establish the complexity of finding and counting elementary modes. We show in particular that finding one elementary mode is easy but that this task becomes hard when a specific EM (i.e. an EM containing some specified reactions) is sought. We then show that counting the number of elementary modes is ♯ P-complete. We emphasize that the easy problems can be solved using currently existing software packages. We then analyse the complexity of a closely related task which is the computation of so-called minimum reaction cut sets and we show that this problem is hard. We then present two positive results which both allow to avoid computing EMs as a prior to the computation of reaction cuts. The first one is a polynomial approximation algorithm for finding a minimum reaction cut set. The second one is a test for verifying whether a set of reactions constitutes a reaction cut; this test can be readily included in existing algorithms to improve their performance. Finally, we discuss the complexity of other cut-related problems.

Abstract: In vitro neural networks of cortical neurons interfaced to a computer via multichannel microelectrode arrays (MEA) provide a unique paradigm to create a hybrid neural computer. Unfortunately, only rudimentary information about these in vitro network's computational properties or the extent of their abilities are known. To study those properties, a liquid state machine (LSM) approach was employed in which the liquid (typically an artificial neural network) was replaced with a living cortical network and the input and readout functions were replaced by the MEA-computer interface. A key requirement of the LSM architecture is that inputs into the liquid state must result in separable outputs based on the liquid's response (separation property). In this paper, high and low frequency multi-site stimulation patterns were applied to the living cortical networks. Two template-based classifiers, one based on Euclidean distance and a second based on a cross-correlation were then applied to measure the separation of the input-output relationship. The result was over a 95% (99.8% when nonstationarity is compensated) input reconstruction accuracy for the high and low frequency patterns, confirming the existence of the separation property in these biological networks.

Abstract: According to the economic and biological aspects of renewable resources management, we propose a Lotka-Volterra predator-prey model with state dependent impulsive harvest. By using the Poincare map, some conditions for the existence and stability of positive periodic solution are obtained. Moreover, we show that there is no periodic solution with order larger than or equal to three under some conditions. Numerical results are carried out to illustrate the feasibility of our main results. The bifurcation diagrams of periodic solutions are obtained by using the numerical simulations, and it is shown that a chaotic solution is generated via a cascade of period-doubling bifurcations, which implies that the presence of pulses makes the dynamic behavior more complex.

Abstract: There are two key characteristic of animal and human societies: (1) degree heterogeneity, meaning that not all individual have the same number of associates; and (2) the interaction topology is not static, i.e. either individuals interact with different set of individuals at different times of their life, or at least they have different associations than their parents. Earlier works have shown that population structure is one of the mechanisms promoting cooperation. However, most studies had assumed that the interaction network can be described by a regular graph (homogeneous degree distribution). Recently there are an increasing number of studies employing degree heterogeneous graphs to model interaction topology. But mostly the interaction topology was assumed to be static. Here we investigate the fixation probability of the cooperator strategy in the prisoner's dilemma, when interaction network is a random regular graph, a random graph or a scale-free graph and the interaction network is allowed to change. We show that the fixation probability of the cooperator strategy is lower when the interaction topology is described by a dynamical graph compared to a static graph. Even a limited network dynamics significantly decreases the fixation probability of cooperation, an effect that is mitigated stronger by degree heterogeneous networks topology than by a degree homogeneous one. We have also found that from the considered graph topologies the decrease of fixation probabilities due to graph dynamics is the lowest on scale-free graphs.

Abstract: The author proposes a kinetic model describing the interplay of messenger ribonucleic acid (mRNA), protein, produced via translation of this RNA, and nonprotein coding RNA (ncRNA). The model includes association of mRNA and ncRNA and regulation of the ncRNA production by protein. In the case of positive feedback between the production of protein and ncRNA, the steady state of the system is found to be unique. For negative feedback, the model predicts in the mean-field case either unique steady state or bistable kinetics. With incorporation of fluctuations, the bistability is manifested in the form of kinetic bursts provided that the number of reactants is low. Basically, the model describes the simplest biological switch operating with participation of ncRNA. Although the results obtained are applicable to ncRNSs in general, the presentation is focused primarily on microRNAs (miRNAs) which form a large important subclass of ncRNAs and are thought to regulate up to one third of all human genes.

Abstract: Here, we put forward a redox molecular hypothesis about the natural biophysical substrate of visual perception and visual imagery. This hypothesis is based on the redox and bioluminescent processes of neuronal cells in retinotopically organized cytochrome oxidase-rich visual areas. Our hypothesis is in line with the functional roles of reactive oxygen and nitrogen species in living cells that are not part of haphazard process, but rather a very strict mechanism used in signaling pathways. We point out that there is a direct relationship between neuronal activity and the biophoton emission process in the brain. Electrical and biochemical processes in the brain represent sensory information from the external world. During encoding or retrieval of information, electrical signals of neurons can be converted into synchronized biophoton signals by bioluminescent radical and non-radical processes. Therefore, information in the brain appears not only as an electrical (chemical) signal but also as a regulated biophoton (weak optical) signal inside neurons. During visual perception, the topological distribution of photon stimuli on the retina is represented by electrical neuronal activity in retinotopically organized visual areas. These retinotopic electrical signals in visual neurons can be converted into synchronized biophoton signals by radical and non-radical processes in retinotopically organized mitochondria-rich areas. As a result, regulated bioluminescent biophotons can create intrinsic pictures (depictive representation) in retinotopically organized cytochrome oxidase-rich visual areas during visual imagery and visual perception. The long-term visual memory is interpreted as epigenetic information regulated by free radicals and redox processes. This hypothesis does not claim to solve the secret of consciousness, but proposes that the evolution of higher levels of complexity made the intrinsic picture representation of the external visual world possible by regulated redox and bioluminescent reactions in the visual system during visual perception and visual imagery.

Abstract: In this theoretical and speculative essay, I propose that insights into certain aspects of neural system functions can be gained from viewing brain function in terms of the branch of Statistical Mechanics currently referred to as "Modern Critical Theory" [Stanley, H.E., 1987. Introduction to Phase Transitions and Critical Phenomena. Oxford University Press; Marro, J., Dickman, R., 1999. Nonequilibrium Phase Transitions in Lattice Models. Cambridge University Press, Cambridge, UK]. The application of this framework is here explored in two stages: in the first place, its principles are applied to state transitions in global brain dynamics, with benchmarks of Cognitive Neuroscience providing the relevant empirical reference points. The second stage generalizes to suggest in more detail how the same principles could also apply to the relation between other levels of the structural-functional hierarchy of the nervous system and between neural assemblies. In this view, state transitions resulting from the processing at one level are the input to the next, in the image of a 'bucket brigade', with the content of each bucket being passed on along the chain, after having undergone a state transition. The unique features of a process of this kind will be discussed and illustrated.

Abstract: On the basis of the general character and operation of the process of perception, a formalism is sought to mathematically describe the subjective or abstract/mental process of perception. It is shown that the formalism of orthodox quantum theory of measurement, where the observer plays a key role, is a broader mathematical foundation which can be adopted to describe the dynamics of the subjective experience. The mathematical formalism describes the psychophysical dynamics of the subjective or cognitive experience as communicated to us by the subject. Subsequently, the formalism is used to describe simple perception processes and, in particular, to describe the probability distribution of dominance duration obtained from the testimony of subjects experiencing binocular rivalry. Using this theory and parameters based on known values of neuronal oscillation frequencies and firing rates, the calculated probability distribution of dominance duration of rival states in binocular rivalry under various conditions is found to be in good agreement with available experimental data. This theory naturally explains an observed marked increase in dominance duration in binocular rivalry upon periodic interruption of stimulus and yields testable predictions for the distribution of perceptual alteration in time.

Abstract: The development of bio-electronic prostheses, hybrid human-electronics devices and bionic robots has been the aim of many researchers. Although neurophysiologic processes have been widely investigated and bio-electronics has developed rapidly, the dynamics of a biological neuronal network that receive sensory inputs, store and control information is not yet understood. Toward this end, we have taken an interdisciplinary approach to study the learning and response of biological neural networks to complex stimulation patterns. This paper describes the design, execution, and results of several experiments performed in order to investigate the behavior of complex interconnected structures found in biological neural networks. The experimental design consisted of biological human neurons stimulated by parallel signal patterns intended to simulate complex perceptions. The response patterns were analyzed with an innovative artificial neural network (ANN), called ITSOM (Inductive Tracing Self Organizing Map). This system allowed us to decode the complex neural responses from a mixture of different stimulations and learned memory patterns inherent in the cell colonies. In the experiment described in this work, neurons derived from human neural stem cells were connected to a robotic actuator through the ANN analyzer to demonstrate our ability to produce useful control from simulated perceptions stimulating the cells. Preliminary results showed that in vitro human neuron colonies can learn to reply selectively to different stimulation patterns and that response signals can effectively be decoded to operate a minirobot. Lastly the fascinating performance of the hybrid system is evaluated quantitatively and potential future work is discussed.

Abstract: Both direct and indirect experimental evidence has shown signaling, communication and conductivity in microtubules (MTs). Theoretical models have predicted that MTs can be potentially used for both classical and quantum information processing although controversies arose in regard to physiological temperature effects on these capabilities. In this paper, MTs have been studied using well-established principles of classical statistical physics as applied to information processing, information storage and signal propagation. To investigate the existence of information processing in MTs we used cellular automata (CA) models with neighbor rules based on the electrostatic properties of the molecular structure of tubulin, and both synchronous and asynchronous updating methods. We obtained a phase diagram of possible dynamic behaviors in MTs that depend on the values of characteristic physical parameters that can be experimentally verified.

Abstract: We consider a model of HIV-1 infection with a reverse transcriptase inhibitor (RTI) therapy and three delays: the first delay is defined as the time from the virus entry into the target cell to the reverse transcriptase step, the second delay represents the time from the virus entry to the production of new viruses and the third delay corresponds to the time necessary for a newly produced virus to become infectious. We analyse the stability of the steady states and determine a threshold value for the first delay at which the system exhibits a Hopf bifurcation. This might explain the clinically observed transient elevated viremia called viral blips. The frequency of the bifurcating periodic solution as well as the threshold value is approximated numerically using realistic parameter. The estimated threshold value is realistic and the frequency of the oscillations is consistent with that of the observed viral blips.

Abstract: In this paper, we study the dynamics of the transmission of respiratory syncytial virus (RSV) in the population using stochastic models. The stochastic models are developed introducing stochastic perturbations on the demographic parameter as well as on the transmission rate of the RSV. Numerical simulations of the deterministic and stochastic models are performed in order to understand the effect of fluctuating birth rate and transmission rate of the RSV on the population dynamics. The numerical solutions of stochastic models are calculated using Euler-Maruyama and Milstein schemes, and confidence intervals for stochastic solutions are given using Monte-Carlo method. Analysis of the numerical results reveals that perturbations on the transmission rate are more decisive in the dynamics of RSV than perturbations on demographic parameters. In addition, the stochastic models show the advantage of reproducing more effectively the noisy RSV hospitalization data. It is concluded that these stochastic models are a viable option to provide a realistic modeling of the RSV dynamics on the population.

Abstract: It is difficult to design electronic nonlinear devices capable of reproducing complex oscillations because of the lack of general constructive rules, and because of stability problems related to the dynamical robustness of the circuits. This is particularly true for current analog electronic circuits that implement mathematical models of bursting and spiking neurons. Here we describe a novel, four-dimensional and dynamically robust nonlinear analog electronic circuit that is intrinsic excitable, and that displays frequency adaptation bursting and spiking oscillations. Despite differences from the classical Hodgkin-Huxley (HH) neuron model, its bifurcation sequences and dynamical properties are preserved, validating the circuit as a neuron model. The circuit's performance is based on a nonlinear interaction of fast-slow circuit blocks that can be clearly dissected, elucidating burst's starting, sustaining and stopping mechanisms, which may also operate in real neurons. Our analog circuit unit is easily linked and may be useful in building networks that perform in real-time.

Abstract: We present an efficient algorithm for individual-based, stochastic simulation of biological populations in continuous time. A simple method for its implementation is given and it is compared to Gillespie's commonly used Direct Method. These two methods are proven to be exactly equivalent and, using a basic evolutionary model, it is demonstrated that the new algorithm can run thousands of times faster. Furthermore, while computational cost per event increases linearly with population size under the Direct Method, this cost is independent of population size under the new algorithm. We argue that this gain in efficiency opens up the possibility to explore a new class of models in population biology.

Abstract: Biology presents incomparable, but desirable, characteristics compared to engineered systems. Inspired by biological development, we have devised a multi-layered design architecture that attempts to capture the favourable characteristics of biological mechanisms for application to design problems. We have identified and implemented essential features of Genetic Regulatory Networks (GRNs) and cell signalling which lead to self-organization and cell differentiation. We have applied this to electronic circuit design.

Abstract: A favorite wing pattern element in butterflies that has been the focus of intense study in evolutionary and developmental biology, as well as in behavioral ecology, is the eyespot. Because the pace of research on these bull's eye patterns is accelerating we sought to develop a tool to automatically detect and measure butterfly eyespot patterns in digital images of the wings. We used a machine learning algorithm with features based on circularity and symmetry to detect eyespots on the images. The algorithm is first trained with examples from a database of images with two different labels (eyespot and non-eyespot), and subsequently is able to provide classification for a new image. After an eyespot is detected the radius measurements of its color rings are performed by a 1D Hough Transform which corresponds to histogramming. We trained software to recognize eyespot patterns of the nymphalid butterfly Bicyclus anynana but eyespots of other butterfly species were also successfully detected by the software.

Abstract: The universe of cellular forms has received scarce attention by mainstream neo-Darwinian views. The possibility that a fundamental trait of biological order may consist upon, or be guided by, developmental processes not completely amenable to natural selection was more akin to previous epochs of biological thought, i.e. the "bauplan" discussion. Thirty years ago, however, Lynn and Tucker studied the biological mechanisms responsible for defining organelles position inside cells. The fact that differentiated structures performing a specific function within the eukaryotic cell (i.e. mitochondrion, vacuole, or chloroplast) were occupying specific positions in the protoplasm was the observational and experimental support of the 'morphogenetic field' notion at the cellular level. In the present paper we study the morphogenetic field evolution yielding from an initial population of undifferentiated cells to diversified unicellular organisms as well as specialized eukaryotic cell types. The cells are represented as Julia sets and Pickover biomorphs, simulating the effect of Darwinian natural selection with a simple genetic algorithm. The morphogenetic field "defines" the locations where cells are differentiated or sub-cellular components (or organelles) become organized. It may be realized by different possibilities, one of them by diffusing chemicals along the Turing model. We found that Pickover cells show a higher diversity of size and form than those populations evolved as Julia sets. Another novelty is the way that cellular organelles and cell nucleus fill in the cell, always in dependence on the previous cell definition as Julia set or Pickover biomorph. Our findings support the existence of specific attractors representing the functional and stable form of a differentiated cell-genuine cellular bauplans. The configuration of the morphogenetic field is "attracted" towards one or another attractor depending on the environmental influences as modeled by a particular fitness function. The model promotes the classical discussions of D'Arcy Thompson and the more recent views of Waddington, Goodwin and others that consider organisms as dynamical systems that evolve through a 'master plan' of transformations, amenable to natural selection. Intriguingly, the model also connects with current developments on mechanobiology, highlighting the informational-developmental role that cytoskeletons may play.

Abstract: Our understanding of the evolution of the insulin signaling pathway (ISP) is still incomplete. One intriguing unanswered question is the explanation of the emergence of the glucostatic role of insulin in mammals. To find out whether this is due to the development of new sets of signaling transduction elements in these organisms, or to the establishment of new interactions between pre-existing proteins, we rebuilt putative orthologous ISPs in 17 eukaryotic organisms. Then, we computed the conservation of orthologous ISPs at different levels, from sequence similarity of orthologous proteins to co-evolution of interacting domains. We found that the emergence of glucostatic role in mammals can neither be explained by the development of new sets of signaling elements, nor by the establishment of new interactions between pre-existing proteins. The comparison of orthologous IRS molecules indicates that only in mammals have they acquired their complete functionality as efficient recruiters of effector sub-pathways.

Abstract: Evidence requiring transcriptase quantum processing is identified and elementary quantum methods are used to qualitatively describe origins and consequences of time-dependent coherent proton states populating informational DNA base pair sites in T4 phage, designated by G–C → G′–C′, G–C → *G–*C and AT → *A–*T. Coherent states at these ‘point’ DNA lesions are introduced as consequences of hydrogen bond arrangement, keto–amino → enol–imine, where product protons are shared between two sets of indistinguishable electron lone-pairs, and thus, participate in coupled quantum oscillations at frequencies of ∼1013 s−1. This quantum mixing of proton energy states introduces stability enhancements of ∼0.25–7 kcal/mole. Transcriptase genetic specificity is determined by hydrogen bond components contributing to the formation of complementary interstrand hydrogen bonds which, in these cases, is variable due to coupled quantum oscillations of coherent enol–imine protons. The transcriptase deciphers and executes genetic specificity instructions by implementing measurements on superposition proton states at G′–C′, *G–*C and *A–*T sites in an interval Δt ≪ 10−13 s. After initiation of transcriptase measurement, model calculations indicate proton decoherence time, τD, satisfies the relation Δt

Abstract: In this paper, we use stickers to construct a solution space of DNA for the maximal clique problem (MCP). Simultaneously, we also apply the DNA operation in the sticker-based model to develop a DNA algorithm. The results of the proposed algorithm show that the MCP is resolved with biological operations in the sticker-based model for the solution space of the sticker. Moreover, this work presents clear evidence of the ability of DNA computing to solve the NP-complete problem. The potential of DNA computing for the MCP is promising given the operational time complexity of O(n × k).

Abstract: We use nonlinear time series analysis methods to analyze the dynamics of the sound-producing apparatus of the American crocodile (Crocodylus acutus). We capture its dynamics by analyzing a recording of the singing activity during mating time. First, we reconstruct the phase space from the sound recording and thereby reveal that the attractor needs no less than five degrees of freedom to fully evolve in the embedding space, which suggests that a rather complex nonlinear dynamics underlies its existence. Prior to investigating the dynamics more precisely, we test whether the reconstructed attractor satisfies the notions of determinism and stationarity, as a lack of either of these properties would preclude a meaningful further analysis. After positively establishing determinism and stationarity, we proceed by showing that the maximal Lyapunov exponent of the recording is positive, which is a strong indicator for the chaotic behavior of the system, confirming that dynamical nonlinearities are an integral part of the examined sound-producing apparatus. At the end, we discuss that methods of nonlinear time series analysis could yield instructive insights and foster the understanding of vocal communication among certain reptile species.

Abstract: The modelling of gene regulatory networks (GRNs) has classically been addressed through very different approaches. Among others, extensions of Thomas's asynchronous Boolean approach have been proposed, to better fit the dynamics of biological systems: genes may reach different discrete expression levels, depending on the states of other genes, called the regulators: thus, activations and inhibitions are triggered conditionally on the proper expression levels of these regulators. In contrast, some fine-grained propositions have focused on the molecular level as modelling the evolution of biological compound concentrations through differential equation systems. Both approaches are limited. The first one leads to an oversimplification of the system, whereas the second is incapable to tackle large GRNs. In this context, hybrid paradigms, that mix discrete and continuous features underlying distinct biological properties, achieve significant advances for investigating biological properties. One of these hybrid formalisms proposes to focus, within a GRN abstraction, on the time delay to pass from a gene expression level to the next. Until now, no research work has been carried out, which attempts to benefit from the modelling of a GRN by differential equations, converting it into a multi-valued logical formalism of Thomas, with the aim of performing biological applications. This paper fills this gap by describing a whole pipelined process which orchestrates the following stages: (i) model conversion from a piece-wise affine differential equation (PADE) modelization scheme into a discrete model with focal points, (ii) characterization of subgraphs through a graph simplification phase which is based on probabilistic criteria, (iii) conversion of the subgraphs into parametric linear hybrid automata, (iv) analysis of dynamical properties (e.g. cyclic behaviours) using hybrid model-checking techniques. The present work is the outcome of a methodological investigation launched to cope with the GRN responsible for the reaction of Escherichia coli bacterium to carbon starvation. As expected, we retrieve a remarkable cycle already exhibited by a previous analysis of the PADE model. Above all, hybrid model-checking enables us to infer temporal properties, whose biological signification is then discussed.

Abstract: Recent analyses of biological and artificial networks have revealed a common network architecture, called scale-free topology. The origin of the scale-free topology has been explained by using growth and preferential attachment mechanisms. In a cell, proteins are the most important carriers of function, and are composed of domains as elemental units responsible for the physical interaction between protein pairs. Here, we propose a model for protein-protein interaction networks that reveals the emergence of two possible topologies. We show that depending on the number of randomly selected interacting domain pairs, the connectivity distribution follows either a scale-free distribution, even in the absence of the preferential attachment, or a normal distribution. This new approach only requires an evolutionary model of proteins (nodes) but not for the interactions (edges). The edges are added by means of random interaction of domain pairs. As a result, this model offers a new mechanistic explanation for understanding complex networks with a direct biological interpretation because only protein structures and their functions evolved through genetic modifications of amino acid sequences. These findings are supported by numerical simulations as well as experimental data.

Abstract: The effect of radiation on a cell population is described by a two-dimensional nonlinear system of differential equations. If the radiation rate is not too high, the system is known to have an asymptotically stable equilibrium. First, for the monitoring of this effect, the concept of observability is applied. For the case when the total number of cells is observed, without distinction between healthy and affected cells, a so-called observer system is constructed, which, at least near the equilibrium state, makes it possible to recover the dynamics of both the healthy and the affected cells, from the observation of the total number of cells without distinction. Results of simulations with illustrative data are also presented. If we want to control the system into a required new equilibrium state, and maintain this new equilibrium by a constant control, a technique of theory of optimal control can be applied to construct a feedback control system.

Abstract: Models are of central importance in many scientific contexts. Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles of living systems. Biological models, such as gene regulatory models, can help us better understand interactions among genes and how cells regulate their production of proteins and enzymes. One feature shared among living systems is their ability to cope with perturbations and remain stable, a property that is the result of evolutionary fine-tuning over many generations. In this study we use random Boolean networks (RBNs) as an abstract model of gene regulatory systems. By applying Differential Evolution (DE), an evolution-based optimization technique, we produce networks with increased stability. DE requires relatively few user-specified parameters, has fast convergence and does not rely on initial conditions to find the global minima within multi-dimensional search spaces. The stability of networks is evaluated by taking parameters such as their network sensitivity, attractor cycle length and number of attractor basins into account. In this study we present an evolutionary approach to produce networks with specific properties (high stability) starting from chaotic regimes. From this chaotic regime and randomly generated classical RBNs with static input degree, our evolutionary approach is able to produce networks with homogenous Boolean functions and highly structured state spaces.

Abstract: The commonly used accumulated payoff scheme is not invariant with respect to shifts of payoff values when applied locally in degree-inhomogeneous population structures. We propose a suitably modified payoff scheme and we show both formally and by numerical simulation, that it leaves the replicator dynamics invariant with respect to affine transformations of the game payoff matrix. We then show empirically that, using the modified payoff scheme, an interesting amount of cooperation can be reached in three paradigmatic non-cooperative two-person games in populations that are structured according to graphs that have a marked degree inhomogeneity, similar to actual graphs found in society. The three games are the Prisoner's Dilemma, the Hawks-Doves and the Stag-Hunt. This confirms previous important observations that, under certain conditions, cooperation may emerge in such network-structured populations, even though standard replicator dynamics for mixing populations prescribes equilibria in which cooperation is totally absent in the Prisoner's Dilemma, and it is less widespread in the other two games.

Abstract: We describe a compact representation of the genetic code that factorizes the table in quartets. It represents a "least grammar" for the genetic language. It is justified by the Klein-4 group structure of RNA bases and codon doublets. The matrix of the outer product between the column-vector of bases and the corresponding row-vector V(T)=(C G U A), considered as signal vectors, has a block structure consisting of the four cosets of the KxK group of base transformations acting on doublet AA. This matrix, translated into weak/strong (W/S) and purine/pyrimidine (R/Y) nucleotide classes, leads to a code table with mixed and unmixed families in separate regions. A basic difference between them is the non-commuting (R/Y) doublets: AC/CA, GU/UG. We describe the degeneracy in the canonical code and the systematic changes in deviant codes in terms of the divisors of 24, employing modulo multiplication groups. We illustrate binary sub-codes characterizing mutations in the quartets. We introduce a decision-tree to predict the mode of tRNA recognition corresponding to each codon, and compare our result with related findings by Jestin and Soule [Jestin, J.-L., Soule, C., 2007. Symmetries by base substitutions in the genetic code predict 2' or 3' aminoacylation of tRNAs. J. Theor. Biol. 247, 391-394], and the rearrangements of the table by Delarue [Delarue, M., 2007. An asymmetric underlying rule in the assignment of codons: possible clue to a quick early evolution of the genetic code via successive binary choices. RNA 13, 161-169] and Rodin and Rodin [Rodin, S.N., Rodin, A.S., 2008. On the origin of the genetic code: signatures of its primordial complementarity in tRNAs and aminoacyl-tRNA synthetases. Heredity 100, 341-355], respectively.

Abstract: Deciphering the knowledge of HIV protease specificity and developing computational tools for detecting its cleavage sites in protein polypeptide chain are very desirable for designing efficient and specific chemical inhibitors to prevent acquired immunodeficiency syndrome. In this study, we developed a generative model based on a generalization of variable order Markov chains (VOMC) for peptide sequences and adapted the model for prediction of their cleavability by certain proteases. The new method, called variable context Markov chains (VCMC), attempts to identify the context equivalence based on the evolutionary similarities between individual amino acids. It was applied for HIV-1 protease cleavage site prediction problem and shown to outperform existing methods in terms of prediction accuracy on a common dataset. In general, the method is a promising tool for prediction of cleavage sites of all proteases and encouraged to be used for any kind of peptide classification problem as well.